Infinity is Really Big

February 12, 2019February 12, 2019

New Video: Immunization, Part 4

In “New Video: Immunization, Part 3“, I showed that if a liability cashflow is not immunized by an asset cashflow, we might be able to make modifications to change this state of affairs.

In particular, the time of payment of one of the asset amounts could be changed to achieve, at least, Redington immunization. To be even … Read the rest

February 8, 2019December 1, 2019

Why Does Slicing a Cone Give an Ellipse?

The intersection of the pink plane with the blue cone is an ellipse (shaded orange when y > 0 and brown when y < 0). The length of either red line added to the length of either yellow line is constant.

Currently my favorite YouTube channel is “3Blue1Brown“, created by Grant Sanderson.

With excellent visuals and high production quality, Grant both shows and explains mathematics in a way that … Read the rest

February 4, 2019February 12, 2019

New Video: Immunization, Part 3

Immunization of a liability cashflow by an asset cashflow can help to cushion a company when interest rates change, but is it always possible?

My most recent video is “Actuarial Exam 2/FM: Liabilities Not Immunized by Assets in Spite of PV and Duration Matching” (Financial Math for Actuarial Exam 2 (FM), Video #171. October 2018 SOA Sample Exam, Problem #127). … Read the rest

February 1, 2019February 1, 2019

New Video: Immunization, Part 2

In the previous post, “New Video: Immunization, Part 1“, I introduced the idea of Redington immunization of liability cashflows by asset cashflows.

It was a post that delved into the details of my previous YouTube video “Actuarial Exam 2/FM Prep: Use Redington Immunization to Find a Ratio of Assets in a Portfolio” embedded … Read the rest

January 30, 2019January 31, 2019

New Video: Immunization, Part 1

It is very important for any business, including any insurance company, to be able to meet their financial liability obligations.

A major class of liabilities that insurance companies must plan for are the claims from their customers. For example, if a person buys car insurance, then the insurance company would be obligated to pay for, among other things, some or … Read the rest

January 28, 2019July 26, 2019

Does the Square Root of Two Exist?

The proof that the square root of two is an irrational number is considered to be one of the most elegant in all of mathematics.

As a formal “If…, then…” statement, it reads: If $x^{2}=2,$ then $x$ is not a rational number. A more informal statement of this is “the square root of two is irrational”.

Rational Numbers

But what is a … Read the rest

January 24, 2019January 28, 2019

New Video: Rebalancing a Bond Portfolio for a New Macaulay Duration

Rebalancing a portfolio is an important kind of financial planning action. It can be done to increase your rate of return or to change the susceptibility of the value of your investments to changes in yield rates.

For a coupon bond, the “duration” or “length” of the bond is a way to measure its susceptibility to … Read the rest

January 22, 2019July 18, 2019

Deconstructing the Mean Value Theorem, Part 3

The Mean Value Theorem implies that there is at least one tangent line with the same slope as the secant line.

Pete Brady strolled out of the U.S. Postal Service office just off Weaver Lake Road in Maple Grove, Minnesota at exactly 10 am.

Coffee and important package in hand, he set off on his 161 mile (259 kilometer) journey … Read the rest

January 18, 2019January 28, 2019

New Video: Derivatives of Bond Prices w.r.t. Parallel Shift in Yield Curve

The series of payments that arises from a coupon bond is an example of a cashflow that can be assigned a “duration“.

A coupon bond can be purchased as an investment that pays “coupons”, which are fixed amounts of money, at certain equally-spaced times during the term of the investment, plus a redemption … Read the rest

January 16, 2019January 28, 2019

Financial Mathematics Terms: Effective Versus Nominal Rates of Interest

One of the most confusing topics for many people when starting to learn about financial mathematics is the various ways of measuring compound interest.

Terms like “effective interest rate”, “nominal interest rate”, “continuous interest rate”, and “real interest rate” show up in various articles and textbooks. Exploring the distinctions and relationships between effective and nominal interest rates is the … Read the rest